First compute the period of the curve:
[tex]\cos(11x)=\cos(11(x+T))\\=\cos(11x+11T )[/tex]
The above equation implies that:
[tex]11x=11x+11T+2k\pi[/tex]
The smallest solution is: [tex]T= \frac{2\pi}{11} [/tex]
First compute the following area:
[tex] \int\limits^{\pi/22}_{-\pi/22} {7\cos(11x)} \, dx = \frac{14}{11} [/tex]
Then compute the following area:
[tex] \left\vert\int\limits^{\pi/22+\pi/11}_{\pi/22} {7\cos(11x)} \, dx\right\vert=\dfrac{14}{11}[/tex]
Adding the two values we get the total area:
[tex]\frac{14}{11}+\frac{14}{11}=\frac{28}{11}[/tex]
